effect of changing point of contact within the boundaries of a cellist’s judgement

is as follows:

Overtone content is maximal when point of contact is fairly close to the

node, that is the bridge and/or the nut and/or either side of the touching

finger.212

Overtone content is minimal when point of contact is at a particular

distance away from any node. This is precisely half the distance from

one node to another, or half the wavelength of the associated harmonic

(i.e. 1/12 of the string for the 6th harmonic, ¼ of the string for the 8th

harmonic).213

Overtone content reduces as the point of contact moves from the

positions associated with the maximal to minimal result.

The ‘overtone-takeover point’ for harmonics is, compared with equivalent

pitches on the stopped string, relatively far from the bridge. In addition, since

there are relatively few partials available to take over the timbre, the noise

element of plucking/striking/bowing close to the bridge becomes very present in

the sound for contact points in this area. Particularly when bowing, the coarse

bow-bridge noise strongly characterises the sound. For high harmonics, this

noise element dominates the sound very quickly after the ‘overtone-takeover’

point. The ‘optimum’ bowing point then, at which maximally overtone-rich

sounds and limited noise are produced, is slightly further from the bridge than a

stopped string of equivalent pitch.

B4 Excitation forceAPPLICATIONS SPECIFIC TO PLUCKING AND STRIKING

The relationship between excitation force and loudness in the case of

harmonics is broadly the same as that of the ‘normal’ stopped string.214

212 The other nodal points for the harmonic in question also maximise overtone content,however, as explained above, these are difficult to find, especially for high harmonics.213 Similarly to the stopped string, this is not strictly true in the case of bowing (see ‘A1 Point ofcontact’). Bowing restricts partials with nodes and antinodes at a particular point (however,bowing close to an antinode allows the partial to vibrate well). This accounts for the certain‘black spots’ found on a string for each harmonic. At these points, antinodes for the associatedharmonic, a light stuttering sound with little or no pitch is heard. For high harmonics, several ofthese ‘black spots’ occur; the number of antinodes for a partial is the same as the partial’sorder; accounting for a rising number of such regular contact points that do not seem to suit theharmonic as harmonic order increases. 214 See ‘A2 String displacement and excitation force’.

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